In this paper we show an efficient method for inducing classifiers that directly optimize the area under the ROC curve. Recently, AUC gained importance in the classification community as a mean to compare the performance of classifiers. Because most classification methods do not optimize this measure directly, several classification learning methods are emerging that directly optimize the AUC. These methods, however, require many costly computations of the AUC, and hence, do not scale well to large datasets. In this paper, we develop a method to increase the efficiency of computing AUC based on a polynomial approximation of the AUC. As a proof of concept, the approximation is plugged into the construction of a scalable linear classifier that directly optimizes AUC using a gradient descent method. Experiments on real-life datasets show a high accuracy and efficiency of the polynomial approximation.